Mathematics, 27.08.2019 02:30 mpete1234567890

Pumps a, b, and c operate at their respective constant rates. pumps a and b, operating simultaneously, can fill a certain tank in 6/5 hours; pumps a and c, operating simultaneously, can fill the tank in 3/2 hours; and pumps b and c, operating simultaneously, can fill the tank in 2 hours. how many hours does it take pumps a, b, and c, operating simultaneously, to fill the tank? a. 1/3 b. 1/2 c. 2/3 d. 5/6 e. 1

Answers: 3

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Answer from: bethzabezarahi

The correct option is E.

Step-by-step explanation:

It is given that pumps A and B, operating simultaneously, can fill a certain tank in 6/5 hours.

One hour work of A and B = 5/6

Pumps A and C, operating simultaneously, can fill the tank in 3/2 hours.

One hour work of A and C = 2/3

Pumps B and C, operating simultaneously, can fill the tank in 2 hours.

One hour work of B and C = 1/2

We need to find the how many hours does it take pumps A, B, and C, operating simultaneously, to fill the tank.

Add one hour work

A and B + A and C + B and C = $\frac{5}{6}+\frac{2}{3}+\frac{1}{2}$

$2A+2B+2C=\frac{5+4+3}{6}$

$2(A+B+C)=\frac{12}{6}$

2(A+B+C)=2

Divide both sides by 2.

(A+B+C)=1

Reciprocal of 1 is 1. It means ABC can fill the tank in 1 hour simultaneously. Therefore the correct option is E.

Answer from: Quest

amount of oatypop that contains the prize = 40%

amount of oatypop which doesn't contain the prize = (100-40)=60%

probability that hannah will win a prize

= s +f s +f f s+ff f s+ff f f s+ infinity.where f= failure,s= success

= or 60%

probability that hannah only has to buy 3 or less boxes before getting a prize= (s) and ( f s) and (ff s) and (f f f s)

= = 87.04 %

step-by-step explanation:

Answer from: Quest

{x = -1/2 , y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer: {x = -1/2 , y = -1

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